surface area of triangular prism 2
TRANSCRIPT
Finding: Surface Area of Triangular Prism 2
- Mr Kim
Please view:
Surface Area of Triangular Prism 1
Before you view this lesson
12 m
15 m
9.4 m
12 m
15 m
9.4 m
Find the Area of all 5 Faces of this Prism
12 m
15 m
9.4 m
Front Area is
12 m
15 m
9.4 m
Front Area is
21
12 m
15 m
9.4 m
Front Area is
121521
12 m
15 m
9.4 m
Since the Back is the same as the
Front…
121521
12 m
15 m
9.4 m
2121521
Times by 2
12 m
15 m
9.4 m
2121521
Now let’s find the Left Side
12 m
15 m
9.4 m
2121521
Add that on
12 m
15 m
9.4 m
2121521
The Left side is a Rectangle
12 m
15 m
9.4 m
We have…
2121521
12 m
15 m
9.4 m
2121521
We have…
12 m
15 m
9.4 m
2121521
But not
12 m
15 m
9.4 m
2121521
We have to find that length
12 m
15 m
9.4 m
2121521
We will call that unknown length
x
x
12 m
15 m
9.4 m
x
To find x we need to use Pythagoras theorem
using the Front Triangle
2121521
12 m
15 m
9.4 m
x
To find x we need to use Pythagoras theorem
using the Front Triangle
2121521
12 m
15 m
9.4 m
x 2121521
12 m
15 m
9.4 m
x
So if we use Pythagoras theorem we will get…
2121521
12 m
15 m
9.4 m
x
So if we use Pythagoras theorem we will get…
x
2121521
12 m
15 m
9.4 m
x
2x
squared
2121521
12 m
15 m
9.4 m
x
2x
Equals
2121521
12 m
15 m
9.4 m
x
152 x
Equals
2121521
12 m
15 m
9.4 m
x
22 15x
squared
2121521
12 m
15 m
9.4 m
x
Now, see how x is the longest side of the
triangle so we…
22 15x
2121521
12 m
15 m
9.4 m
x
22 15x
Now, see how x is the longest side of the
triangle so we PLUS
2121521
15 m
9.4 m
x
121522 x
12 m
2121521
12
15 m
9.4 m
x
222 1215 x
squared
12 m
2121521
12 m
15 m
9.4 m
x
222 1215 x
so x equals…x
2121521
12 m
15 m
9.4 m
x
222 1215 xxsquare root…
2121521
12 m
15 m
9.4 m
x
222 1215 xxof the whole thing
2121521
12 m
15 m
9.4 m
x
222 1215 x22 1215 xof the whole thing
2121521
12 m
15 m
9.4 m
x
222 1215 xBecause the opposite
of squared…
22 1215 x
2121521
12 m
15 m
9.4 m
x
222 1215 x22 1215 xis square root
2121521
12 m
15 m
9.4 m
x
222 1215 xPutting this in the calculator gives…
22 1215 x
2121521
12 m
15 m
9.4 m
x
222 1215 xPutting this in the calculator gives…
22 1215 x2.19x
2121521
12 m
15 m
9.4 m
222 1215 xSo the unknown length is 19.2 m
22 1215 x2.19x
2121521 19.2
m
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
Now let’s find the Area of the Left
Side
2121521
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
Now let’s find the Area of the Left
Side
2121521
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
2.194.9
2121521
Now let’s find the Area of the Left
Side
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
2.194.9
Now find the Area of the Right Side
2121521
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
2.194.9
2121521
Add that on
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
So the Area of the Right Side is
2.194.9
2121521
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
12
2.194.9
2121521
So the Area of the Right Side is
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
So the Area of the Right Side is
12
2.194.9
2121521
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
If it’s 9.4 m there
12
2.194.9
2121521
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
12
9.4 m 2.194.9
2121521
It’s 9.4 m there as well
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
4.912
9.4 m 2.194.9
2121521
It’s 9.4 m there as well
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
4.912
9.4 m
And finally, find the Bottom Area
2.194.9
2121521
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
4.912
9.4 m 2.194.9
2121521
Add that on
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
9.4 m
Bottom Area
4.912 2.194.9
2121521
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
9.4 m
154.9
4.912 2.194.9
2121521
Bottom Area
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
9.4 m
154.9
4.912 2.194.9
2121521
Putting this altogether in the calculator
gives…
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
9.4 m
23.614154.9 m
4.912 2.194.9
2121521
Putting this altogether in the calculator
gives…
Our Final Answer!